A 44-year-man was detained on Tuesday under the Terrorism Act and remains in custody.
Police earlier confirmed that a 45-year-old man had also been arrested overnight.
A republican parade to commemorate the 1916 Easter Rising took place in Derry on Monday.
It was connected to the group Saoradh, which is accused of having links with the New IRA.
The Parades Commission had ruled that no paramilitary-style clothing be worn in the procession.
The Unfinished Revolution National Easter Commemoration parade ended at Derry City Cemetery where an address was delivered.
There were reports of disturbances at the cemetery on Monday evening.
Police confirmed that officers had come under attack as they made arrests.
Five men, aged 29, 38, 40, 50 and 54, were arrested under the Terrorism Act.
Another man, aged 40, has been charged after being arrested on suspicion of disorderly behaviour and resisting police.
He is due to appear at Londonderry Magistrates’ Court on May 11.
Officers also seized a number of vehicles, suspected terrorist uniforms and petrol bombs.
The men detained on suspicion of terrorism offences remained in custody on Tuesday afternoon.
Police Service of Northern Ireland (PSNI) officers also carried out searches in the Creggan area of the city on Tuesday.